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Use the properties of logarithms to find the derivative. Hint: It might be easier if you use the properties of logarithms first.$$y=\log _{3} x^{2}$$

$$\frac{2}{x \ln 3}$$

Algebra

Chapter 4

Exponential and Logarithmic Functions

Section 6

Properties of Logarithmic Functions

Oregon State University

McMaster University

Baylor University

Idaho State University

Lectures

02:07

Use the properties of loga…

02:15

03:11

02:22

01:59

02:09

01:18

01:19

01:22

01:11

Use logarithmic differenti…

02:55

So our task is to find the derivative of log based three of X squared. Now, what I would do is ah, rewrite this problem with that too. In front eso are looking at This is one of the law of logs Log based three of X And then from here I would use the change based formulas because I don't like to memorize more than I have to. I would just rewrite this as natural log of X over natural log of three on the reason why this is helpful is then I could rewrite this because natural log of three is just a constant. Um, I like to put my constant together so that, too, is in the numerator, not over natural log of three times natural log. Becks. So now that I'm asked to find the derivative do you y dx? Well, because we have a constant times a function because, remember, I don't know what natural log of three is, but it's just the same number over and over again. Um, so a constant times a function, the derivative of it is that constant times the derivative of this function. So I'm looking at two over natural log of three times the derivative of natural log of X is one over X. Well, typically, people don't like seeing like is a natural log of three times X or is a natural log of the quantity of three X. And that's why they'll write the answer with the X in front because multiplication is communicative. Um, and then this will be our final answer. So the derivative of that function is to over X natural log of three.

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